SOLUTION: ASAP HELP!(^)I use this symbol to represent exponents I have a question, if the loudness level of a sound, D, in decibels, is given by the formula D= 10 log (10^12 I) where I is

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: ASAP HELP!(^)I use this symbol to represent exponents I have a question, if the loudness level of a sound, D, in decibels, is given by the formula D= 10 log (10^12 I) where I is      Log On


   

Question 80892: ASAP HELP!(^)I use this symbol to represent exponents
I have a question, if the loudness level of a sound, D, in decibels, is given by the formula D= 10 log (10^12 I) where I is the intensity of the sound, in watts per meter^2. Decibel levels range from 0, a barely audible sound, to 160, a sound resulting in a ruptured eardrum. What is the decibel level of a normal conversation, 3.2 x 10^-6 watt per meter^2?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If your decibel formula is

Simply plug in into I




Group the terms and




Since we're multiplying two like bases with exponents we can add the exponents



add the exponents

Break up the logs by using this identity
We can clearly see that (since this is always true ) so it reduces to



Now use your calculator to find . It comes to 0.50515

So our problem reduces further to




Add

Multiply

So an intensity of 3.2 x 10^-6 watt per meter^2 means the decibel measure is about 65.015 decibels. For more problems dealing with decibels check out this decibel calculator. You'll need to use the calculator on the far right.